The present invention relates to methods for analyzing and/or designing structural systems with damping. More particularly in one form, the present invention relates to methods for analyzing and designing wheels and other cyclic symmetric structures of gas turbine engines such that there is damping of one or more vibratory responses of the wheel assembly, or such that a particular excitation is no longer aliasingly coupled into one or more vibratory modal responses. Although the present invention was developed for analyzing gas turbine engine components, it has application to analyzing cyclic symmetric structures in other fields of technology.
The deleterious effects of forced resonant vibration are well known. Structures often show lightly damped vibratory response at their resonant frequencies. When the resonant response is forced by an excitation at the same frequency, the structure is often subjected to high cycle fatigue (HCF) stresses in excess of the HCF stress limit of the material of the structure, with subsequent breakage.
In a gas turbine engine, structures such as wheels of the turbine and compressor section are sometimes analyzed so as to better understand their dynamic response. Further, wheel assemblies and other gas turbine engine structures are sometimes exposed to substantial amounts of testing as components, subassemblies and complete engines. During this analysis and testing, it may be that the resonant frequencies of the wheel assembly respond not just to the frequency of the excitation, but also the manner in which the excitation couples into the mode shape of the wheel assembly. For example, a particular vibratory mode shape may respond strongly with greatly amplified motion at its resonant frequency when excited at that frequency by a specific multiple of the engine rotational speed. However, that same vibratory mode shape may show greatly reduced response when excited at the same frequency by a different multiple of engine operation. In addition, that same vibratory mode may show greatly reduced response if excited at the same frequency and multiple of engine operation and the mode is no longer aliasingly coupled to the multiple of engine operation.
When a lightly damped, highly amplified response exists within the speed range of the engine, it is sometimes necessary to take corrective action to prevent breakage of the wheel assembly. This corrective action could include stiffening of the wheel assembly so that the resonant frequency of the vibratory mode of interest is raised outside of the engine operating range. Unfortunately, a wheel redesigned to be stiffer may also be heavier. In other situations, it may be necessary to alter the components in the flow path upstream of the wheel assembly. However, this alteration may be expensive.
What is needed then, is a method of analyzing and designing wheel assemblies and other components to alter their vibrational characteristics with minimal impact on weight and cost. The present invention accomplishes this and other needs in a novel and unobvious way.
Briefly describing one aspect of the present invention, there is a cyclically symmetric structure that is associated with a rotating device, and wherein an integral multiple of the rotational speed of the rotating device resonates a first natural frequency of the cyclically symmetric structure. Periodic discontinuities may be introduced into the structure such that the integral multiple of rotational speed can be made to aliasingly couple into a second natural frequency, and no longer couple, or minimally couple, into the first natural frequency.
Briefly describing another aspect of the present invention, there is a contemplated method for analyzing and/or designing a cyclically symmetric structure that includes preparing a finite element model of the cyclically symmetric structure which includes a model of a frictional interface. A frictional interface stress or deflection is predicted for the vibratory response of the model with the structure arranged in a first asymmetry. After rearranging the structure in a second asymmetry, the frictional interface stress or deflection is recomputed. The frictional interface stress or deflection from the first asymmetry is compared with the frictional interface stress or deflection of the second asymmetry, and the structural arrangement having the asymmetry with the higher stress or deflection is selected.
Briefly describing one aspect of the present invention, there is a gas turbine engine with a wheel assembly, wherein an integral multiple of the rotational speed of the engine resonates a first natural frequency of a wheel assembly, the wheel assembly comprising a wheel and a plurality of blades. The blades may be grouped such that the integral multiple of rotational speed no longer resonates the first natural frequency. By grouping the blades, the integral multiple of rotational speed can be made to aliasingly couple into a second natural frequency, and no longer couple, or only weakly couple, into the first natural frequency.
Briefly describing another aspect of the present invention, there is a method for designing a gas turbine engine that includes preparing a finite element model of a wheel assembly which includes a model of a coupling. A coupling stress is predicted for the vibratory response of the model with the blades of the wheel assembly grouped in a first pattern. After regrouping the blades in a second pattern, the coupling stress is recomputed. The coupling stresses from the first pattern are compared to the coupling stresses from the second pattern, and the pattern with the higher stress is selected.
These and other aspects of the present invention will be apparent from the drawings, description of the preferred embodiment, and the claims to follow.